Originally Posted by
Zorak
On FT these are known as First Class Monetization or FCM offers* They will typically appear on the individual itinerary, although availability depends on revenue management algorithms. You can also click on the seat map and see if seats in a higher cabin are available for selection, in which case clicking on one will reveal the current price (you can choose cash or miles) to purchase an upgraded seat. Note that if you want to upgrade your entire trip in one direction it can often be cheaper (sometimes significantly) to just change your ticket to a first class ticket instead, so if you are considering an FCM offer it is worth doing a new flight search and seeing what it would cost to buy F from the get-go instead. (EDIT: although less likely on an international trip I think.)
*See:
First Class Monetization, or FCM: The Definitive Thread (and/or the mods may decide to merge this thread into that one)
I pretty confident you won't see DL FCM offers on KL coded DL flights due to the nature of these offers which reclass flights in a different DL booking class without doing a re-issue. It's possible there might be some sort of day of departure upgrade offer that does not modify booking class, but I kind of doubt it.